Finding Polynomials with Integer Coefficients & \sqrt(2) + i Zero

[duki]

Homework Statement

Find a polynomial with integer coefficient for which $$\sqrt(2) + i$$ is a zero.

Homework Equations

The Attempt at a Solution

I'm not sure where to really start with this one. It is on my review sheet, and I can't remember how to do it. Could someone give me a hand?

 

[GregA]

Homework Statement

Find a polynomial with integer coefficient for which $$\sqrt(2) + i$$ is a zero.

Homework Equations

The Attempt at a Solution

I'm not sure where to really start with this one. It is on my review sheet, and I can't remember how to do it. Could someone give me a hand?

consider (sqrt(2)+i)²...what are you left with after expanding and simplifying?
how about (sqrt(2)+i)⁴?

 

[duki]

Ok, as an answer I got:

$$x^2 - 2 \sqrt{2}x + 2 - i$$
Does that look right?

 

[duki]

Latex isn't working, so I got

x^2 - 2sqrt(2)x + 2 - i